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6

An upper limit to the photon fraction in

cosmic rays above 1019 eV from the Pierre

Auger Observatory

J. Abraham6, M. Aglietta41, C. Aguirre8, D. Allard73,

I. Allekotte1, P. Allison69, C. Alvarez44, J. Alvarez-Muniz58,M. Ambrosio38, L. Anchordoqui68, 79, J.C. Anjos10, C. Aramo38,

K. Arisaka72, E. Armengaud22, F. Arneodo42, F. Arqueros56,

T. Asch28, H. Asorey1, B.S. Atulugama70, J. Aublin21,M. Ave73, G. Avila3, J. Bacelar49, T. Backer32, D. Badagnani5,

A.F. Barbosa10, H.M.J. Barbosa13, M. Barkhausen26,D. Barnhill72, S.L.C. Barroso10, P. Bauleo63, J. Beatty69,

T. Beau22, B.R. Becker77, K.H. Becker26, J.A. Bellido78,S. BenZvi64, C. Berat25, T. Bergmann31, P. Bernardini36,

X. Bertou1, P.L. Biermann29, P. Billoir24, O. Blanch-Bigas24,

F. Blanco56, P. Blasi35, C. Bleve 61, H. Blumer31, P. Boghrat72,M. Bohacova20, C. Bonifazi10, R. Bonino41, M. Boratav24,

J. Brack74, J.M. Brunet22, P. Buchholz32, N.G. Busca73,K.S. Caballero-Mora31, B. Cai75, D.V. Camin37,

J.N. Capdevielle22, R. Caruso43, A. Castellina41, G. Cataldi36,L. Cazon73, R. Cester40, J. Chauvin25, A. Chiavassa41,

J.A. Chinellato13, A. Chou65, J. Chye67, D. Claes76,P.D.J. Clark60, R.W. Clay7, S.B. Clay7, B. Connolly64,A. Cordier23, U. Cotti46, S. Coutu70, C.E. Covault62,

J. Cronin73, S. Dagoret-Campagne23, T. Dang Quang80,P. Darriulat80, K. Daumiller27, B.R. Dawson7,

R.M. de Almeida13, L.A. de Carvalho13, C. De Donato37,S.J. de Jong48, W.J.M. de Mello Junior13,

J.R.T. de Mello Neto17, I. De Mitri36, M.A.L. de Oliveira15,V. de Souza12, L. del Peral57, O. Deligny21, A. Della Selva38,

C. Delle Fratte39, H. Dembinski30, C. Di Giulio39, J.C. Diaz67,C. Dobrigkeit 13, J.C. D’Olivo47, D. Dornic21, A. Dorofeev66,

M.T. Dova5, D. D’Urso38, M.A. DuVernois75, R. Engel27,

Preprint

L. Epele5, M. Erdmann30, C.O. Escobar13, A. Etchegoyen3,A. Ewers26, P. Facal San Luis58, H. Falcke51, 48, A.C. Fauth13,

D. Fazio43, N. Fazzini65, A. Fernandez44, F. Ferrer62, S. Ferry55,B. Fick67, A. Filevich3, A. Filipcic55, I. Fleck32, E. Fokitis33,

R. Fonte43, D. Fuhrmann26, W. Fulgione41, B. Garcıa6,D. Garcia-Pinto56, L. Garrard63, X. Garrido23, H. Geenen26,

G. Gelmini72, H. Gemmeke28, A. Geranios34, P.L. Ghia41,M. Giller53, J. Gitto6, H. Glass65, F. Gobbi6, M.S. Gold77,

F. Gomez Albarracin5, M. Gomez Berisso1,

R. Gomez Herrero57, M. Goncalves do Amaral18, J.P. Gongora6,D. Gonzalez31, J.G. Gonzalez68, M. Gonzalez45, D. Gora52, 31,

A. Gorgi41, P. Gouffon11, V. Grassi37, A. Grillo42, C. Grunfeld5,C. Grupen32, F. Guarino38, G.P. Guedes14, J. Gutierrez57,

J.D. Hague77, J.C. Hamilton24, M.N. Harakeh49, D. Harari1,S. Harmsma49, S. Hartmann26, J.L. Harton63, M.D. Healy72,

T. Hebbeker30, D. Heck27, C. Hojvat65, P. Homola52,

J. Horandel31, A. Horneffer48, M. Horvat55, M. Hrabovsky20,M. Iarlori35, A. Insolia43, M. Kaducak65, O. Kalashev72,

K.H. Kampert26, B. Keilhauer31, E. Kemp13, H.O. Klages27,M. Kleifges28, J. Kleinfeller27, R. Knapik63, J. Knapp61,

D.-H. Koang25, Y. Kolotaev32, A. Kopmann28, O. Kromer28,S. Kuhlman65, J. Kuijpers48, N. Kunka28, A. Kusenko72,

C. Lachaud22, B.L. Lago17, D. Lebrun25, P. LeBrun65, J. Lee72,A. Letessier-Selvon24, M. Leuthold30,69, I. Lhenry-Yvon21,G. Longo38, R. Lopez44, A. Lopez Aguera58, A. Lucero6,

S. Maldera41, M. Malek65, S. Maltezos33, G. Mancarella36,M.E. Mancenido5, D. Mandat20, P. Mantsch65, A.G. Mariazzi61,

I.C. Maris31, D. Martello36, N. Martinez5, J. Martınez45,O. Martınez44, H.J. Mathes27, J. Matthews66, 71,

J.A.J. Matthews77, G. Matthiae39, G. Maurin22, D. Maurizio40,P.O. Mazur65, T. McCauley68, M. McEwen66, R.R. McNeil66,

G. Medina47, M.C. Medina3, G. Medina Tanco12, A. Meli29,D. Melo3, E. Menichetti40, A. Menshikov28, Chr. Meurer27,R. Meyhandan66, M.I. Micheletti3, G. Miele38, W. Miller77,

S. Mollerach1, M. Monasor56, 57, D. Monnier Ragaigne23,

2

F. Montanet25, B. Morales47, C. Morello41, E. Moreno44,C. Morris69, M. Mostafa78, M.A. Muller13, R. Mussa40,

G. Navarra41, L. Nellen47, C. Newman-Holmes65, D. Newton58,T. Nguyen Thi80, R. Nichol69, N. Nierstenhofer26, D. Nitz67,

H. Nogima13, D. Nosek19, L. Nozka20, J. Oehlschlager27,T. Ohnuki72, A. Olinto73, L.F.A. Oliveira17,

V.M. Olmos-Gilbaja58, M. Ortiz56, S. Ostapchenko27, L. Otero6,M. Palatka20, J. Pallotta6, G. Parente58, E. Parizot21,

S. Parlati42, M. Patel61, T. Paul68, K. Payet25, M. Pech20,

J. Pekala52, R. Pelayo45, I.M. Pepe16, L. Perrone36, S. Petrera35,P. Petrinca39, Y. Petrov63, D. Pham Ngoc80, T.N. Pham Thi80,

R. Piegaia5, T. Pierog27, O. Pisanti38, T.A. Porter66,J. Pouryamout26, L. Prado Junior13, P. Privitera39,

M. Prouza64, E.J. Quel6, J. Rautenberg26, H.C. Reis12,S. Reucroft68, B. Revenu22, J. Rıdky20, A. Risi6, M. Risse27,

C. Riviere25, V. Rizi35, S. Robbins26, M. Roberts70,

C. Robledo44, G. Rodriguez58, D. Rodrıguez Frıas57,J. Rodriguez Martino39, J. Rodriguez Rojo39, G. Ros56, 57,

J. Rosado56, M. Roth27, C. Roucelle24, B. Rouille-d’Orfeuil24,E. Roulet1, A.C. Rovero2, F. Salamida35, H. Salazar44,

G. Salina39, F. Sanchez3, M. Santander4, E.M. Santos10,S. Sarkar59, R. Sato4, V. Scherini26, T. Schmidt31,

O. Scholten49, P. Schovanek20, F. Schussler27, S.J. Sciutto5,M. Scuderi43, D. Semikoz22, G. Sequeiros40, R.C. Shellard10,

B.B. Siffert17, G. Sigl22, P. Skelton61, W. Slater72,

N. Smetniansky De Grande3, A. Smia lkowski53, R. Smıda20,B.E. Smith61, G.R. Snow76, P. Sokolsky78, P. Sommers70,

J. Sorokin7, H. Spinka65, E. Strazzeri39, A. Stutz25, F. Suarez41,T. Suomijarvi21, A.D. Supanitsky3, J. Swain68,

Z. Szadkowski26,53, A. Tamashiro2, A. Tamburro31, O. Tascau26,R. Ticona9, C. Timmermans48, 50, W. Tkaczyk53,

C.J. Todero Peixoto13, A. Tonachini40, D. Torresi43,P. Travnicek20, A. Tripathi72, G. Tristram22,

D. Tscherniakhovski28, M. Tueros5, V. Tunnicliffe60, R. Ulrich27,

M. Unger27, M. Urban23, J.F. Valdes Galicia47, I. Valino58,

3

L. Valore38, A.M. van den Berg49, V. van Elewyck21,R.A. Vazquez58, D. Veberic55, A. Veiga5, A. Velarde9,

T. Venters73, V. Verzi39, M. Videla6, L. Villasenor46,T. Vo Van80, S. Vorobiov22, L. Voyvodic65, H. Wahlberg5,

O. Wainberg3, T. Waldenmaier31, P. Walker60, D. Warner63,A.A. Watson61, S. Westerhoff64, C. Wiebusch26, G. Wieczorek53,

L. Wiencke78, B. Wilczynska52, H. Wilczynski52, C. Wileman61,M.G. Winnick7, J. Xu28, T. Yamamoto73, P. Younk67, E. Zas58,

D. Zavrtanik55, M. Zavrtanik55, A. Zech24, A. Zepeda45,

M. Zha61, M. Ziolkowski32

(1) Centro Atomico Bariloche (CNEA); Instituto Balseiro (CNEA and UNCuyo);CONICET, 8400 San Carlos de Bariloche, Rıo Negro, Argentina

(2) Instituto de Astronomıa y Fısica del Espacio (CONICET), CC 67, Suc. 28(1428) Buenos Aires, Argentina

(3) Laboratorio Tandar (CNEA); CONICET; Univ. Tec. Nac. (Reg. BuenosAires), Av. Gral. Paz 1499, (1650) San Martın, Buenos Aires, Argentina

(4) Pierre Auger Southern Observatory, Av. San Martin Norte 304, (5613)Malargue, Prov. De Mendoza, Argentina

(5) Universidad Nacional de la Plata, Facultad de Ciencias Exactas,Departamento de Fısica and IFLP/CONICET; Univ. Nac. de Buenos Aires,

FCEyN, Departamento de Fısica, C.C. 67, (1900) La Plata, Argentina(6) Universidad Tecnologica Nacional, Regionales Mendoza y San Rafael;

CONICET; CEILAP-CITEFA, Rodrıguez 273 Mendoza, Argentina(7) University of Adelaide, Dept. of Physics, Adelaide, S.A. 5005, Australia

(8) Universidad Catolica de Bolivia, Av. 16 Julio 1732, POB 5829, La Paz, Bolivia(9) Universidad Mayor de San Andres, Av. Villazon N 1995, Monoblock Central,

Bolivia(10) Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, CEP

22290-180 Rio de Janeiro, RJ, Brazil(11) Universidade de Sao Paulo, Inst. de Fisica, Cidade Universitaria Caixa

Postal 66318, Caixa Postal 66318, 05315-970 Sao Paulo, SP, Brazil(12) Universidade de Sao Paulo, Instituto Astronomico e Geofisico, Cidade

Universitaria, Rua do Matao 1226, 05508-900 Sao Paulo, SP, Brazil(13) Universidade Estadual de Campinas, Gleb Wataghin Physics Institute

(IFGW), Departamento de Raios Cosmicos e Cronologia, CP 6165, 13083-970,Campinas, SP, Brazil

(14) Univ. Estadual de Feira de Santana, Departamento de Fisica, CampusUniversitario, BR 116, KM 03, 44031-460 Feira de Santana, Brazil

(15) Universidade Estadual do Sudoeste da Bahia (UESB), Dep. Ciencias Exatas,Estrada do Bem-Querer km4, 45083-900, Vitoria da Conquista, BA, Brazil

(16) Universidade Federal da Bahia, Campus da Ondina, 40210-340 Salvador,BA, Brazil

(17) Univ. Federal do Rio de Janeiro (UFRJ), Instituto de Fısica, Cidade

4

Universitaria, Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil(18) Univ. Federal Fluminense, Inst. de Fisica, Campus da Praia Vermelha,

24210-340 Niteroi, RJ, Brazil(19) Charles University, Institute of Particle & Nuclear Physics, Faculty of

Mathematics and Physics, V Holesovickach 2, CZ-18000 Prague 8, Czech Republic(20) Institute of Physics of the Academy of Sciences of the Czech Republic, Na

Slovance 2, CZ-182 21 Praha 8, Czech Republic(21) Institut de Physique Nucleaire, Universite Paris-Sud 11 and IN2P3/CNRS,

15, rue Georges Clemenceau, 91400 Orsay, France(22) Laboratoire AstroParticule et Cosmologie, Universite Paris VII, 11, Place

Marcelin Berthelot, F-75231 Paris CEDEX 05, France(23) Laboratoire de l’Accelerateur Lineaire, Universite Paris- Sud 11 and

IN2P3/CNRS, BP 34, Batiment 200, F-91898 Orsay cedex, France(24) Laboratoire de Physique Nucleaire et de Hautes Energies, Universite Paris 6

& 7 and IN2P3/CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France(25) Laboratoire de Physique Subatomique et de Cosmologie (LPSC),

IN2P3/CNRS, Universite Joseph-Fourier (Grenoble 1), 53, ave. des Martyrs,F-38026 Grenoble CEDEX, France

(26) Bergische Universitat Wuppertal, Fachbereich C - Physik, GaußStr. 20, D -42097 Wuppertal, Germany

(27) Forschungszentrum Karlsruhe, Institut fur Kernphysik, Postfach 3640, D -76021 Karlsruhe, Germany

(28) Forschungszentrum Karlsruhe, Institut fur Prozessdatenverarbeitung undElektronik, Postfach 3640, D - 76021 Karlsruhe, Germany

(29) Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D - 53121Bonn, Germany

(30) RWTH Aachen, III. Physikalisches Institut A, Physikzentrum, Huyskensweg,D - 52056 Aachen, Germany

(31) Universitat Karlsruhe (TH), Institut fur Experimentelle Kernphysik (IEKP),Postfach 6980, D - 76128 Karlsruhe, Germany

(32) Universitat Siegen, Fachbereich 7 Physik - Experimentelle Teilchenphysik,Emmy Noether-Campus, Walter-Flex-Str. 3, D - 57068 Siegen, Germany(33) Physics Department, School of Applied Sciences, National Technical

University of Athens, Zografou 15780, Greece(34) Physics Department, Nuclear and Particle Physics Section, University of

Athens, Ilissia 15771, Greece(35) Dipartimento di Fisica dell’Universita de l’Aquila and INFN, Via Vetoio,

I-67010 Coppito, Aquila, Italy(36) Dipartimento di Fisica dell’Universita di Lecce and Sezione INFN, via

Arnesano, I-73100 Lecce, Italy(37) Dipartimento di Fisica dell’Universita di Milano and Sezione INFN, via

Celoria 16, I-20133 Milan, Italy(38) Dipartimento di Fisica dell’Universita di Napoli and Sezione INFN, Via

Cintia 2, 80123 Napoli, Italy(39) Dipartimento di Fisica dell’Universita di Roma II ”Tor Vergata” and Sezione

INFN, Via della Ricerca Scientifica, I- 00133 Roma, Italy(40) Dipartimento di Fisica Sperimentale dell’Universita di Torino and Sezione

5

INFN, Via Pietro Giuria, 1, I-10125 Torino, Italy(41) Istituto di Fisica dello Spazio Interplanetario (INAF), sezione di Torino andDipartimento di Fisica Generale dell’Universita and INFN Torino, Via P. Giuria

1, 10125 Torino, Italy(42) INFN, Laboratori Nazionali del Gran Sasso, Strada Statale 17/bis Km

18+910, I-67010 Assergi (L’Aquila), Italy(43) Dipartimento di Fisica dell’Universita di Catania and Sezione INFN, Corso

Italia, 57, I-95129 Catania, Italy(44) Benemerita Universidad Autonoma de Puebla (BUAP), Ap. Postal J – 48,

72500 Puebla, Puebla, Mexico(45) Centro de Investigacion y de Estudios Avanzados del IPN (CINVESTAV),

Apartado Postal 14-740, 07000 Mexico, D.F., Mexico(46) Universidad Michoacana de San Nicolas de Hidalgo (UMSNH), Edificio C-3

Cd Universitaria, C.P. 58040 Morelia, Michoacan, Mexico(47) Universidad Nacional Autonoma de Mexico (UNAM), Apdo. Postal 20-364,

01000 Mexico, D.F., Mexico(48) Department of Astrophysics, IMAPP, Radboud University, 6500 GL

Nijmegen, Netherlands(49) Kernfysisch Versneller Instituut (KVI), Rijksuniversiteit Groningen,

Zernikelaan 25, NL-9747 AA Groningen, Netherlands(50) NIKHEF, POB 41882, NL-1009 DB Amsterdam, Netherlands

(51) ASTRON, PO Box 2, 7990 AA Dwingeloo, Netherlands(52) Institute of Nuclear Physics PAN, Radzikowskiego 52, 31- 342 Cracow,

Poland(53) University of Lodz, Pomorska 149/153, 90 236 Lodz, Poland

(54) LIP Laboratorio de Instrumentacao e Fısica Experimental de Partıculas,Avenida Elias Garcia, 14-1, P-1000-149 Lisboa, Portugal

(55) University of Nova Gorica, Laboratory for Astroparticle Physics, Vipavska13, POB 301, SI-5000 Nova Gorica, Slovenia

(56) Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de CienciasFisicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain

(57) Space Plasmas and Astroparticle Group, Universidad de Alcala, Pza. SanDiego, s/n, 28801 Alcala de Henares (Madrid), Spain

(58) Departamento de Fısica de Partıculas, Campus Sur, Universidad, E-15782Santiago de Compostela, Spain

(59) Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OxfordOX1 3NP, United Kingdom

(60) Institute of Integrated Information Systems, School of Electronic Engineering,University of Leeds, Leeds LS2 9JT, United Kingdom

(61) School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT,United Kingdom

(62) Case Western Reserve University, Dept. of Physics, Cleveland, OH 44106,United States

(63) Colorado State University, Department of Physics, Fort Collins, CO 80523,United States

(64) Columbia University, Dept. of Physics, New York, NY 10027, United States(65) Fermilab, MS367, POB 500, Batavia, IL 60510-0500, United States

6

(66) Louisiana State University, Dept. of Physics and Astronomy, Baton Rouge,LA 70803-4001, United States

(67) Michigan Technological University, Physics Dept., 1400 Townsend Drive,Houghton, MI 49931-1295, United States

(68) Northeastern University, Department of Physics, 110 Forsyth Street, Boston,MA 02115-5096, United States

(69) Ohio State University, 2400 Olentangy River Road, Columbus, OH43210-1061, United States

(70) Pennsylvania State University, Department of Physics, 104 Davey Lab,University Park, PA 16802-6300, United States

(71) Southern University, Dept. of Physics, Baton Rouge, LA 70813-0400, UnitedStates

(72) University of California, Los Angeles (UCLA), Department of Physics andAstronomy, Los Angeles, CA 90095, United States

(73) University of Chicago, Enrico Fermi Institute, 5640 S. Ellis Ave., Chicago,IL 60637, United States

(74) University of Colorado, Physics Department, Boulder, CO 80309-0446,United States

(75) University of Minnesota, School of Physics and Astronomy, 116 Church St.SE, Minneapolis, MN 55455, United States

(76) University of Nebraska, Dept. of Physics and Astronomy, 116 Brace Lab,Lincoln, NE 68588-0111, United States

(77) University of New Mexico, Dept. of Physics and Astronomy, 800 Yale,Albuquerque, NM 87131, United States

(78) University of Utah, 115 S. 1400 East # 201, Salt Lake City, UT 84112-0830,United States

(79) University of Wisconsin-Milwaukee, Dept. of Physics, Milwaukee, WI 53201,United States

(80) Institute for Nuclear Science and Technology (INST), 5T- 160 Hoang QuocViet Street, Nghia Do, Cau Giay, Hanoi, Vietnam

Abstract

An upper limit of 16% (at 95% c.l.) is derived for the photon fraction in cosmicrays with energies greater than 1019 eV, based on observations of the depth of showermaximum performed with the hybrid detector of the Pierre Auger Observatory. Thisis the first such limit on photons obtained by observing the fluorescence light profileof air showers. This upper limit confirms and improves on previous results fromthe Haverah Park and AGASA surface arrays. Additional data recorded with theAuger surface detectors for a subset of the event sample support the conclusion thata photon origin of the observed events is not favored.

7

1 Introduction

The origin of ultra-high energy (UHE) cosmic rays above 1019 eV is still un-known [1]. Their energy spectrum, arrival directions and composition canbe inferred from air shower observations. However, agreement has not yetbeen reached on whether there is a break in the energy spectrum aroundEGZK ∼ 6× 1019 eV (= 60 EeV). Such a steepening in the energy spectrum isexpected if UHE cosmic rays come from cosmologically distant sources [2], asis suggested by their overall isotropy. There have been claims, as yet uncon-firmed, for clustering on small angular scales, and correlations with possibleclasses of sources. Moreover, results concerning the nuclear composition arestill inconclusive.

While this deficit of robust observational results is partly due to the extremelysmall fluxes and, correspondingly, small numbers of events at such high ener-gies, discrepancies might arise also from the different experimental techniquesused. For instance, the determination of the primary energy from the groundarray alone relies on the comparison with air shower simulations and is thusprone to uncertainties in modelling high energy interactions. Therefore it is es-sential to test results from air shower observations independently. The presentwork provides just such a cross-check for the upper limit derived previouslyfrom ground arrays on the photon fraction in UHE cosmic rays. An upperlimit is set on the photon fraction above 10 EeV which is twice as strong asthose given previously.

Photons are expected to dominate over nucleon primaries in non-acceleration(“top-down”) models of UHE cosmic-ray origin [3,4,5] which have been invokedin particular to account for a continuation of the flux above EGZK without aspectral feature as indicated by AGASA data [6]. Thus, the determinationof the photon contribution is a crucial probe of cosmic-ray source models.Separating photon-induced showers from events initiated by nuclear primariesis experimentally much easier than distinguishing light and heavy nuclearprimaries. As an example, average depths of shower maxima at 10 EeV primaryenergy are predicted to be about 1000 g cm−2, 800 g cm−2, and 700 g cm−2

for primary photons, protons, and iron nuclei, respectively. Moreover, analysesof nuclear composition are uncertain due to our poor knowledge of hadronicinteractions at very high energies. Photon showers, being driven mostly byelectromagnetic interactions, are less affected by such uncertainties and canbe modelled with greater confidence. To avoid the uncertainty from modellinghadronic interactions, we adopt an analysis method that does not require thesimulation of nuclear primaries but compares data to photon simulations only.

So far limits on the UHE photon fraction in cosmic rays have been set byground arrays alone. By comparing the rates of near-vertical showers to in-

8

clined ones recorded by the Haverah Park shower detector, upper limits (95%c.l.) of 48% above 10 EeV and 50% above 40 EeV were deduced [7]. Based onan analysis of muons in air showers observed by the Akeno Giant Air ShowerArray (AGASA), the upper limits (95% c.l.) to the photon fraction were esti-mated to be 28% above 10 EeV and 67% above 32 EeV [8]. An upper limit of67% (95% c.l.) above 125 EeV was derived in a dedicated study of the highestenergy AGASA events [9].

In this work, we obtain a photon limit from the direct observation of the showerprofile with fluorescence telescopes, using the depth of shower maximum Xmax

as the discriminating observable. To achieve a high accuracy in reconstructingthe shower geometry, we make use of the “hybrid” detection technique, i.e.we select events observed by both the ground array and the fluorescence tele-scopes [10]. For a subset of the event sample, a sufficient number of grounddetectors were also triggered, yielding a variety of additional shower observ-ables. Considering as example the signal risetime measured with the groundarray, we demonstrate the discrimination power of these independent observ-ables to photon-induced showers.

The plan of the paper is as follows. In Section 2, predictions for the UHEphoton fraction in cosmic-ray source models and features of photon-initiatedair showers are summarized. Section 3 contains the description of the data andof photon simulations. In particular, the data selection criteria are discussed.A careful choice of the quality and fiducial volume cuts is required to control apossible experimental bias for photon primaries. In Section 4, the method forderiving a photon fraction is described and applied to the data. An exampleof the discrimination power of observables registered by the surface array isshown in Section 5. Finally in Section 6, we discuss the prospects for improvingthe bound on UHE photons.

2 Photons as cosmic-ray primaries

The theoretical challenge of explaining acceleration of protons to the highestenergies is circumvented in non-acceleration models [3]. A significant fractionof the UHE cosmic rays are predicted by these models to be photons (see e.g.[4,5]). For instance, UHE photons may be produced uniformly in the universeby the decay/annihilation of relic topological defects (TD) [11]. During prop-agation to Earth, they interact with background radiation fields and mostof them cascade down to GeV energies where the extragalactic photon fluxis constrained by the EGRET experiment; the remaining UHE photons cancontribute to the cosmic-ray flux above 10 EeV. By contrast in the SuperHeavy Dark Matter (SHDM) model [12], the UHE photons are generated inthe decay of relic metastable particles (such as “cryptons” [13]) which are

9

0.01

0.1

1

10

100

1e+19 1e+20 1e+21

j(E)

E2 [e

V c

m-2

s-1

sr-1

]

E [eV]

P

SHDM p

SHDM

γSHDM

Fig. 1. Example of a SHDM model fit to AGASA data [6] (in the highest andthird highest energy bins which have zero events, upper flux limits are shown).The spectra of photons (γ

SHDM) and protons (p

SHDM) from SHDM, and an assumed

additional nucleonic component at lower energy (P), as well as their sum is plotted.Photons dominate above ∼ 5 × 1019 eV. (Figure taken from [5].)

clustered as cold dark matter in our Galaxy. Since the halo is believed to beeffectively transparent to such UHE photons, they would be directly observedat Earth with little processing. In the Z-Burst (ZB) scenario [14], photons aregenerated from the resonant production of Z bosons by UHE cosmic neutrinosannihilating on the relic neutrino background. A distinctive feature of all thesemodels is the prediction of a large photon flux at high energies, as is expectedfrom considerations of QCD fragmentation [15]. As an illustration, Figure 1(taken from [5]) shows a SHDM model fit to the highest energy AGASA events;photons are the dominant particle species above ∼ 5 × 1019 eV.

Photons can also be produced in “conventional” acceleration models by theGZK-type process from π0 decays. Typically, the corresponding photon fluxesare relatively small. For instance, based on the spectrum obtained by theHiRes experiment [16], the expected photon fraction is only of order 1% orbelow [5].

It should be noted that the photon flux arriving at Earth for a specific sourcemodel is subject to uncertainties arising from photon propagation: assump-tions concerning the very low frequency (few MHz) radio background andinter-galactic magnetic fields must be made [4,5]. The typical range of en-ergy loss lengths usually adopted for photons are 7–15 Mpc at 10 EeV and

10

Elab (eV) ÿ

<Xm

ax>

(g c

m-2

)

proton

iron

photon

photonwith preshower

QGSJET 01

QGSJET II

SIBYLL 2.1

Fly´s EyeHiRes-MIAHiRes 2004Yakutsk 2001Yakutsk 2005CASA-BLANCAHEGRA-AIROBICCSPASE-VULCANDICETUNKA

400

500

600

700

800

900

1000

1100

1200

1014

1015

1016

1017

1018

1019

1020

1021

Fig. 2. Average depth of shower maximum <Xmax> versus energy simulated for pri-mary photons, protons and iron nuclei. Depending on the specific particle trajectorythrough the geomagnetic field, photons above ∼ 5×1019 eV can create a pre-shower:as indicated by the splitting of the photon line, the average Xmax values then do notonly depend on primary energy but also arrival direction. For nuclear primaries, cal-culations for different hadronic interaction models are displayed (QGSJET 01 [17],QGSJET II [18], SIBYLL 2.1 [19]). Also shown are experimental data (for referencesto the experiments, see [20]).

5–30 Mpc at 100 EeV.

Ultra-high energy photons can be detected by the particle cascades they ini-tiate when entering the atmosphere of the Earth. Compared to air showersinitiated by nuclear primaries, photon showers at energies above 10 EeV arein general expected to have a larger depth of shower maximum Xmax and tocontain fewer secondary muons. The latter is because the mean free pathsfor photo-nuclear interactions and direct muon pair production are more thantwo orders of magnitude larger than the radiation length. Consequently, only asmall fraction of the primary energy in photon showers is generally transferredinto secondary hadrons and muons.

In Figure 2, simulated Xmax values for showers initiated by primary photons,protons and iron nuclei are shown as a function of the primary energy. Thelarge Xmax values for photon showers at 10 EeV are essentially due to the smallmultiplicity in electromagnetic interactions, in contrast to the large numberof secondaries produced in inelastic interactions of high-energy hadrons. Sec-ondly, because of the LPM effect [21], the development of photon showers iseven further delayed above ∼ 10 EeV. Another feature of the LPM effect is

11

an increase of shower fluctuations: Xmax fluctuations for photon showers are∼ 80 g cm−2 at 10 EeV, compared to ∼ 60 g cm−2 and ∼ 20 g cm−2 forprimary protons and iron nuclei, respectively.

At higher energies, cosmic-ray photons may convert in the geomagnetic fieldand create a pre-shower before entering the atmosphere [22]. The energythreshold for geomagnetic conversion is ∼ 50 EeV for the Auger southernsite. Conversion probability and pre-shower features depend both on primaryenergy and arrival direction. In the case of a pre-shower, the subsequent airshower is initiated as a superposition of lower-energy secondary photons andelectrons. For air showers from converted photons, the Xmax values and thefluctuations are considerably smaller than from single photons of same totalenergy. From the point of view of air shower development, the LPM effect andpre-shower formation compete with each other.

In this work, cascading of photons in the geomagnetic field is simulated withthe PRESHOWER code [23] and shower development in air, including theLPM effect [21], is calculated with CORSIKA [24]. For photo-nuclear pro-cesses, we assume the extrapolation of the cross-section as given by the Par-ticle Data Group [25], and we employed QGSJET 01 [17] as a hadron eventgenerator.

3 The Data Set

The Auger data used in this analysis were taken with a total of 12 fluorescencetelescopes situated at two different sites [26], during the period January 2004to February 2006. The number of surface detector stations deployed [27] grewduring this period from about 150 to 950. A detailed description of the AugerObservatory is given in [28].

For the present analysis, we selected hybrid events, i.e. showers observed bothwith (one or more) surface tanks and telescopes. Even when only one tank istriggered, the angular accuracy improves from ≥ 2◦ for observation with onetelescope alone to ∼ 0.6◦ for hybrid detection [10,29], thus reducing signifi-cantly the corresponding uncertainty in the reconstruction of Xmax.

The reconstruction of the shower profiles [26,30] is based on an end-to-end cali-bration of the fluorescence telescopes [31]. Monthly models for the atmosphericdensity profiles are used which were derived from local radio soundings [32].An average aerosol model is adopted based on measurements of the local at-mospheric aerosol content [33]. Cloud information is provided by IR monitors,positioned at the telescope stations [33]. Cross-checks on clouds are obtainedfrom measurements with LIDAR systems (near the telescopes) and with a

12

laser facility near the center of the array [33,34]. The Cherenkov light contri-bution of the shower is calculated according to [35]. An energy deposit profileis reconstructed for each event. A Gaisser-Hillas function [36] is fitted to theprofile to obtain the depth of shower maximum, and the calorimetric showerenergy is obtained by integration. It has been checked that this function pro-vides a reasonable description of the simulated shower profiles independent ofthe primary particle, provided all four parameters of the Gaisser-Hillas fit areallowed to vary.

A correction for missing energy, the “invisible” energy fraction carried byneutrinos and high-energy muons, has to be applied. The fraction of missingenergy depends on the primary particle type. In case of nuclear primaries, thecorrection amounts to 7–14%, with a slight dependence on primary energy andthe hadronic interaction model used [37,38]. For photon primaries, the missingenergy fraction is much smaller and amounts to ∼ 1% [38]. We applied thecorrection assuming photon primaries, so that the energy threshold chosen inthe analysis corresponds to the effective energy of primary photons.

For the current analysis, the differences between the energy estimates for dif-ferent primaries are relatively small (∼ 10%) due to the near-calorimetricmeasurement of the primary energy by the fluorescence technique. Moreover,relative to photon showers, the energies of nuclear primaries are slightly under-estimated. This would slightly deplete an event sample from showers ascribedto nuclear primaries or, correspondingly, increase the number ascribed to pho-tons. Thus, the limit derived here for photons is conservative with respect tothe missing energy correction. It seems worthwhile to mention that for groundarray studies, where the energy of photons can be underestimated by morethan 30% (see, for instance, [8]), such corrections to the primary energy whichdepend on the unknown primary particle type must be treated with particularcaution.

The following quality cuts are applied for event selection (in Appendix A,distributions of cut variables are displayed):

• Quality of hybrid geometry: distance of closest approach of the recon-structed shower axis to the array tank with the largest signal <1.5 km,and difference between the reconstructed shower front arrival time at thistank and the measured tank time <300 ns;

• Primary energy E>1019 eV;• Xmax observed;• Number of phototubes in the fluorescence detector triggered by shower ≥6;• Quality of Gaisser-Hillas (GH) profile fit: χ2(GH) per degree of freedom <6,

and χ2(GH)/χ2(line)<0.9, where χ2(line) refers to a straight line fit;• Minimum viewing angle of shower direction towards the telescope >15◦;• Cloud monitors confirm no disturbance of event observation by clouds.

13

Care must be taken about a possible bias against photon primaries of thedetector acceptance. In Figure 3 we show the acceptance for photons andnuclear primaries at different steps of the analysis, computed using showersimulations with the CONEX code [39] which reproduces well the CORSIKApredictions for shower profiles. Light emission and propagation through theatmosphere and the detector response were simulated according to [40]. Ascan be seen from the Figure, the acceptances are comparable for all types ofprimaries after trigger (top plot). However, after profile quality cuts (middleplot) the detection efficiency for photons is smaller by a factor ∼2 than fornuclear primaries, because primary photons reach shower maximum at suchlarge depths (of about 1000 g cm−2, see Figure 2) that for a large fraction ofshowers the maximum is outside the field of view of the telescopes. This holds,in particular, for near-vertical photon showers: since the Auger Observatoryis located at an average atmospheric depth of 880 g cm−2 (measured at apoint close to the centre of the array) near-vertical photon showers reach theground before being fully developed. Such photon showers are rejected by thequality cuts, while most of the showers generated by nuclear primaries (withtheir smaller Xmax) are accepted. An illustration of the effect of this cut onphoton showers is given in Figure 4. To reduce the corresponding bias againstphotons, near-vertical events are excluded in the current analysis. Since theaverage depth of shower maximum increases with photon energy before theonset of pre-shower, a mild dependence of the minimum zenith angle withenergy is chosen (see below).

For similar reasons, a cut on distant events is introduced. The telescopes donot observe shower portions near the horizon, as the field of view is elevatedby ∼ 1.5◦. Thus, the atmospheric depth which corresponds to the lower edgeof the field of view of a telescope decreases with distance. Another source ofa bias against photon showers is due to fluorescence light absorption. Thebrightest parts of the shower profile, i.e. those around shower maximum, arefor photon showers generally closer to the ground. The line of sight towardsthe shower maximum traverses regions of higher air density. Hence, for similargeometrical distances to the shower maximum, the light signal of the deeperphoton showers is more attenuated than for nuclear primaries. The conse-quence is that the distance range below which the telescopes are fully efficientfor detecting showers of a given energy, is smaller for photon primaries thanfor nuclear primaries. This range increases with primary energy. Thus, anenergy-dependent distance cut is applied for the data selection, in addition toexcluding showers at small zenith angles:

• Zenith angle >35◦ + g1(E), with g1(E) = 10(lg E/eV−19.0)◦ for lg E/eV≤19.7 and g1(E) = 7◦ for lg E/eV>19.7;

• Maximum distance of telescope to shower impact point <24 km + g2(E),with g2(E) = 12(lg E/eV−19.0) km.

14

E (EeV)10 100

rela

tive

exp

osu

re

0

0.5

1

1.5

2

2.5

proton

ironphoton

E (EeV)10 100

rela

tive

exp

osu

re

0

0.5

1

1.5

2

2.5

proton

ironphoton

E (EeV)10 100

rela

tive

exp

osu

re

0

0.5

1

1.5

2

2.5

proton

ironphoton

Fig. 3. Relative exposures for photon, proton, and iron primaries as a function ofenergy after trigger (top), after quality cuts (middle) and after fiducial volume cutsare applied (bottom) to reduce the bias against photons. A reference value of oneis adopted for proton at 10 EeV.

The acceptances after the fiducial volume cuts are applied are shown in Fig-ure 3 (bottom plot). The differences between photons and nuclear primaries

15

rejected

fluorescencetelescope

shower profileshower direction

field of view

depth of shower maximum

acceptedevent

event

Fig. 4. Photon showers and the selection requirement of observing Xmax. Fornear-vertical photon showers, Xmax is below the field of view of the telescopes;possibly the showers even reach ground before being fully developed as in the ex-ample shown. Such photon showers were rejected by the quality cuts. The situationchanges when regarding more inclined photon events. The slant atmospheric depththat corresponds to the lower edge of the field of view increases with zenith. Xmax

can then be reached within the field of view, and the photon showers pass the Xmax

quality cut. Requiring a minimum zenith angle in the analysis, the reconstructionbias for photons is strongly reduced.

are now significantly reduced, with the acceptances being comparable at ener-gies 10–20 EeV. With increasing energy, the acceptance for nuclear primariesshows a modest growth, while the photon acceptance is quite flat in the in-vestigated energy range. Only a minor dependence on the nuclear particletype (proton or iron) is seen. Comparing photons to nuclear primaries, theminimum ratio of acceptances is ǫmin ≃ 0.80 at energies 50–60 EeV. At evenhigher energies, the pre-shower effect becomes increasingly important, andacceptances for photons and nuclear primaries become more similar.

The acceptance curves shown in Figure 3 can be used to correct for the detec-tor acceptance when comparing a measured photon limit to model predictions,using the model energy spectra as an input. Since the acceptance ratios afterthe fiducial volume cuts are not far from unity, and since the photon ac-ceptance is quite flat in the energy range below 100 EeV, the correspondingcorrections are expected to be relatively small and to differ very little betweentypical model predictions. In this work, to obtain an experimental limit tothe photon fraction without relying on assumptions on energy spectra of dif-ferent primaries, a correction to the photon limit is applied by conservatively

16

0

5

10

15

20

25

30

35

500 600 700 800 900 1000 1100 1200

atmospheric depth X (g cm-2)

dE/d

X (

1015

eV/(

g cm

-2)) Event 1687849

E ~ 16 EeVXmax~ 780 g cm-2

Fig. 5. Example of a reconstructed longitudinal energy deposit profile (points) andthe fit by a Gaisser-Hillas function (line).

adopting the minimum ratio of acceptances ǫmin (a detailed derivation of theapproach is given in Appendix B).

Applying the cuts to the data, 29 events with energies greater than 10 EeVsatisfy the selection criteria. Due to the steep cosmic-ray spectrum, manyevents in the sample do not exceed 20 EeV. The main shower characteristicsare summarised for all events in Table 1. Figure 5 shows the longitudinalprofile of an event reconstructed with 16 EeV and Xmax = 780 g cm−2. TheXmax distribution of the selected events is displayed in Figure 6.

For the conditions of the highest-energy event in the sample, event 737165(see also [41]) with a reconstructed energy of 202 EeV assuming primary pho-tons, the probability of photon conversion in the geomagnetic field is ∼ 100%.Consequently, the simulated value of the average depth of shower maximumis relatively small, and shower fluctuations are considerably reduced.

It should be noted that the event list given in Table 1 results from selectioncriteria optimized for the current primary photon analysis. These data cannotbe used for studies such as elongation rate measurements without properlyaccounting for acceptance biases. For instance, the minimum zenith anglerequired in this analysis depletes the data sample from showers with relativelysmall depths of shower maximum, with the effect being dependent on primaryenergy.

The uncertainty ∆Xmax of the reconstructed depth of shower maximum is

17

Table 1Event identifier, primary energy, and depth of shower maximum Xmax for the

selected events. Also given are the mean depth of shower maximum <Xγmax> and

its rms fluctuation ∆Xγmax predicted from simulations assuming primary photons.

In the last column, the differences ∆γ (in standard deviations) between photonprediction and data are listed (see text). A caveat is given in the text concerningthe use of these data for elongation rate studies.

Event ID Energy Xmax <Xγmax> ∆Xγ

max ∆γ

[x1018 eV] [g cm−2] [g cm−2] [g cm−2] [std. dev.]

668949 17 765 985 71 2.9

673409 12 760 996 82 2.7

705583 11 678 973 77 3.6

737165 202 821 948 27 3.3

828057 13 805 978 68 2.4

829526 12 727 996 85 3.0

850018 54 774 1050 120 2.2

931431 24 723 1022 89 3.2

935108 14 717 992 68 3.8

986990 15 810 1000 87 2.1

1109855 16 819 1019 95 2.0

1171225 15 786 993 74 2.6

1175036 17 780 1001 100 2.1

1257649 10 711 971 76 3.2

1303077 13 709 992 85 3.1

1337921 18 744 1029 93 2.9

1421093 25 831 1028 93 2.0

1535139 15 768 998 77 2.8

1539432 12 787 975 76 2.3

1671524 13 806 978 77 2.1

1683620 20 824 1035 80 2.5

1683856 18 763 981 92 2.3

1684651 12 753 991 79 2.8

1687849 16 780 1001 71 2.9

1736288 10 726 981 71 3.3

1826386 17 747 994 84 2.8

1978675 10 740 978 76 2.9

2035613 11 802 998 90 2.1

2036381 27 782 1057 101 2.6

composed of several contributions, some of which may vary from event toevent. In this work, we adopt conservative, overall estimates for the currentstatistical and systematic uncertainties which are applied to all selected events.These uncertainties are expected to decrease significantly in the future. How-ever, even when adopting conservative estimates, the present analysis is not

18

0

0.002

0.004

0.006

0.008

0.01

650 700 750 800 850 900Xmax (g cm-2)

1/N

dN

/dX

max

Fig. 6. Distribution of Xmax values of the 29 selected events.

limited by the measurement uncertainties but by event statistics. This is dueto the fact that shower fluctuations for photons are considerably larger thanthe measurement uncertainties.

Main contributions to ∆Xmax are the uncertainties in the profile fit, in showergeometry and in atmospheric conditions (see Table 2). Uncertainties in theXmax reconstruction from atmospheric conditions arise from using averagemodels of the density profiles (monthly averages) and of the aerosol content.The effect on Xmax is studied by changing the atmospheric models and re-peating the event reconstruction. The statistical uncertainty in the determi-nation of the average model results in a systematic uncertainty of the Xmax

reconstruction; it amounts to ∼ 8 g cm−2 (∼ 3 g cm−2 from density pro-files, ∼ 7 g cm−2 from aerosol model). A larger uncertainty comes from thespread around the averages due to time variations of atmospheric conditions(a detailed discussion of the density profile variations can be found in [32]).This results in a statistical uncertainty of the reconstructed Xmax value of∼ 12 g cm−2 (∼ 6 g cm−2 from density profiles, ∼ 10 g cm−2 from aerosolmodel).

An uncertainty in the Xγmax values predicted from photon simulations re-

sults from the uncertainty in the reconstructed primary energy. Currently,the systematic uncertainty in energy is 25% [26]. For an elongation rate of∼ 130 g cm−2 per energy decade for photons above 10 EeV, this correspondsto a systematic uncertainty of ∼ 13 g cm−2. The elongation rate for primaryphotons (see Figure 2) is relatively large here due to the LPM effect. At high-est energies, the elongation rate decreases with the onset of photon pre-shower

19

Table 2Conservative estimates of the contributions to the statistical and systematic un-

certainty of depth of shower maximum for the data and for the photon simulations.

Data ∆Xstatmax [g cm−2] ∆X

systmax [g cm−2]

Profile fit 20 10

Atmosphere 12 8

Geometry reconstruction 10 5

Others 10 5

Simulation

Reconstructed energy of event 5 13

Photo-nuclear cross-section - 10

Hadron generator - 5

Total 28 23

in the geomagnetic field.

It should be noted that this contribution to the systematic uncertainty fromthe energy reconstruction does not refer to the observed Xmax value itself.Rather, it enters indirectly in the analysis since the primary energy is neededas simulation input.

Another uncertainty comes from the extrapolation of the photo-nuclear cross-section to high energy. Larger values than adopted here for the cross-sectionwould make showers initiated by photons more similar to nuclear primariesand reduce the predicted values for Xγ

max. Based on recent theoretical work onthe maximum possible rise of the photo-nuclear cross-section with energy [42]an uncertainty of ∼ 10 g cm−2 is estimated for the predicted depths of showermaximum for photons [43].

Contrary to the case of nuclear primaries, uncertainties from modelling high-energy hadron interactions are much less important in primary photon show-ers. From simulations using different hadron event generators, an uncertaintyof ∼ 5 g cm−2 is adopted.

Adding in quadrature the individual contributions (see Table 2) gives a statis-tical uncertainty ∆Xstat

max ≃ 28 g cm−2 and a systematic uncertainty ∆Xsystmax ≃

23 g cm−2.

For each event, 100 showers were simulated as photon primaries. Since photonshower features can depend in a non-trivial way on arrival direction and energy,

20

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

700 800 900 1000 1100 1200 1300

Xmax (g cm-2)

1/N

dN

/dX

max

Event 1687849:

data photon simulation

Fig. 7. Xmax measured in the shower shown in Figure 5 (point with error bar)compared to the X

γmax distribution expected for photon showers (solid line).

the specific event conditions were adopted for each event. Results of the photonsimulations are also listed in Table 1.

4 Results

In Figure 7 the predictions for Xγmax for a photon primary are compared with

the measurement of Xmax = 780 g cm−2 for event 1687849 (Figure 5). With〈Xγ

max〉 ≃ 1000 g cm−2, photon showers are on average expected to reachmaximum at depths considerably greater than that observed for real events.Shower-to-shower fluctuations are large due to the LPM effect. For this event,the expectation for a primary photon differs by ∆γ ≃ +2.9 standard deviationsfrom the data, where ∆γ is calculated from

∆γ =< Xγ

max > −Xmax√

(∆Xγmax)2 + (∆Xstat

max)2. (1)

For all events, the observed Xmax is well below the average value expected forphotons (see Table 1). The differences ∆γ between photon prediction and datarange from +2.0 to +3.8 standard deviations, see Figure 8 and Table 1. It isextremely unlikely that all 29 events were initiated by photons (probability≪10−10), so an upper limit to the fraction of cosmic-ray photons above 10 EeVcan be reliably set.

21

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5∆γ

1/N

dN

/d∆ γ

Fig. 8. Distribution of differences ∆γ in standard deviations between primary pho-ton prediction and data for the 29 selected events.

Due to the limited event statistics, the upper limit cannot be smaller thana certain value. The relation between the minimum possible fraction fmin

γ ofphotons that could be excluded for a given number of events nm (or: theminimum number of events nmin

m required to possibly exclude a fraction fγ) isgiven by

fminγ = 1 − (1 − α)1/nm , and nmin

m =ln(1 − α)

ln(1 − fγ), (2)

with α being the confidence level of rejection. This holds for the case that noefficiency correction has to be applied (ǫmin = 1). For 29 events and ǫmin ≃ 0.80,the minimum possible value for an upper limit to be set at a 95% confidencelevel is ∼ 12%. The theoretical limit is reached only if a photon origin isbasically excluded for all events.

The calculation of the upper limit is based on the statistical method introducedin [9] which is tailor-made for relatively small event samples. For each event,trial values χ2 = ∆2

γ are calculated with ∆γ according to Eq. (1). We distin-guish between statistical and systematic uncertainties for the depths of showermaximum. The method in [9] is extended to allow for a correlated shift of theobserved Xmax values for all selected events, where the shifted value is drawnat random from a Gaussian distribution with a width ∆Xsyst

max = 23 g cm−2.For the shifted data, new χ2 values are calculated from Eq. (1). Many such“shifted” event sets are generated from the data and compared to artificial

22

0102030405060708090

100

E0 (EeV)

phot

on f

ract

ion

(%)

for

E>E

0

10 30 100

limits at 95% c.l.

A1

A1

HP HP

A2

Auger

SHDM

ZB

TD

SHDM’

Fig. 9. Upper limits (95% c.l.) to the cosmic-ray photon fraction derived in thepresent analysis (Auger) and obtained previously from AGASA (A1) [8], (A2) [9]and Haverah Park (HP) [7] data, compared to expectations for non-accelerationmodels (ZB, SHDM, TD from [5], SHDM’ from [13]).

data sets using photon simulations. The chance probability p(fγ) is calculatedto obtain artificial data sets with χ2 values larger than observed as a functionof the hypothetical primary photon fraction fγ. Possible non-Gaussian showerfluctuations are accounted for in the method, as the probability is constructedby a Monte Carlo technique. The upper limit ful

γ , at a confidence level α, isthen obtained from p(fγ ≥ ǫminf

ulγ ) ≤ 1 − α, where the factor ǫmin = 0.80 ac-

counts for the different detector acceptance for photon and nuclear primaries(Section 3).

For the Auger data sample, an upper limit to the photon fraction of 16% ata confidence level of 95% is derived. In Figure 9, this upper limit is plottedtogether with previous experimental limits and some illustrative estimates fornon-acceleration models. We have shown two different expectations for SHDMdecay [5,13] to illustrate the sensitivity to assumptions made about the decaymode and the fragmentation, as well as the normalisation of the spectrum(see Figure 1). The derived limit is the first one based on observing the depthof shower maximum with the fluorescence technique. The result confirms andimproves previous limits above 10 EeV that came from surface arrays. It isworth mentioning that this improved limit is achieved with only 29 eventsabove 10 EeV, as compared to about 50 events in the Haverah Park analysisand about 120 events in the AGASA analysis.

23

5 Discrimination power of surface array observables

In the current analysis, data from the surface array are used only to achievea high precision of reconstructed shower geometry in hybrid events. A singletank was sufficient for this. However, observables registered by the surfacearray are also sensitive to the primary particle type and can be exploitedfor studies of primary photon showers. In spite of the incomplete coverage ofthe array during the data taking period considered here (which means manyevents were poorly contained), for about half of the selected events a standardarray reconstruction [27] can be performed. Several observables can then beused for primary photon discrimination, for instance the lateral distributionor the curvature of the shower front [44].

An example for another observable is given by the risetime of the showersignal in the detectors, one measure of the time spread of particles in theshower disc. For each triggered tank, we define a risetime as the time for theintegrated signal to go from 10% to 50% of its total value. By interpolationbetween risetimes recorded by the tanks at different distances to the showercore, the risetime at 1000 m core distance is extracted after correcting forazimuthal asymmetries in the shower front. The risetime is sensitive to theprimary particle type because of its correlation with shower muons and thedepth of shower maximum: contrary to the shower muons, electrons undergosignificant deflections with corresponding time delays. Thus, larger values forthe risetime are observed if the signal at ground is dominated by the elec-tromagnetic shower component. Primary photon showers generally have fewermuons and, additionally, the shower maximum is closer to ground comparedto showers from nuclear primaries. Correspondingly, risetimes are expected tobe relatively large for photon primaries.

For the specific event shown in Figure 5, the measured risetime is compared tothe simulated distribution in Figure 10. For this and the other hybrid eventswith array reconstruction, the observed risetime does not agree well with thepredictions for primary photons, supporting the conclusion that a photon ori-gin of the observed events is not favored. In future photon analyses, the inde-pendent information on the primary particle from the Auger ground array andfluorescence telescope data can be used to cross-check each other. Combiningthe different shower observables will further improve the discrimination powerto photons.

24

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 100 200 300 400 500 600 700

risetime t (ns)

1/N

dN

/dt

(per

ns)

Event 1687849:

data photon simulation

Fig. 10. Example of risetime measured in an individual shower, same as in Figure 5(point with error bar) compared to the risetime distribution expected for photonshowers (solid line).

6 Outlook

The upper limit to the photon fraction above 10 EeV derived in this workfrom the direct observation of the shower maximum confirms and reducesprevious limits from ground arrays. The current analysis is limited mainly bythe small number of events. The number of hybrid events will considerablyincrease over the next years, and much lower primary photon fractions can betested. Moreover, the larger statistics will allow us to increase the thresholdenergy above 10 EeV where even larger photon fractions are predicted by somemodels.

As an example, let us consider an increase in data statistics above 10 EeV byabout an order of magnitude compared to the current analysis, as is expectedto be reached in 2008/2009. From Eq. (2), a sensitivity to photon fractionsdown to ∼ 1.5% can be inferred. More realistically, let us assume for themeasured Xmax values a distribution similar to the one currently observedas in Figure 8. Then, an upper limit of ∼ 5% could be achieved. With theincreased run time, a comparable number of events as for the present analysiswould be reached above 30–35 EeV. If an upper limit similar to that reachedhere was found, but at this higher energy, it would be well below existinglimits and severely constrain non-acceleration models. 1

1 A 36% upper limit above 100 EeV has been claimed recently from combining

25

The sensitivity of the hybrid analysis might be further improved in the futureby combining different shower observables measured in the same event, suchas depth of shower maximum, risetime and curvature. We did not includeground array observables for the limit derived in this analysis since we wantedto independently check previous ground array results. Further information,e.g. the width of the shower profile, might also be added in future work toachieve better separation of deeply penetrating nuclear primaries and primaryphotons.

If only surface detector data is used and hybrid detection is not requiredthen the event statistics are increased by about an order of magnitude. Caremust however be taken about a possible bias against photons in an array-onlyanalysis because of the different detector acceptance for photon and nuclearprimaries. Also, compared to the near-calorimetric energy determination in thefluorescence technique, the energy estimated from array data shows a strongerdependence on the primary type and is more strongly affected by showerfluctuations. Ways to reduce a possible photon bias and to place robust limitsto photons are being investigated. For instance, the technique introduced in [7]of comparing event rates of near-vertical and inclined showers can be furtherexploited.

Acknowledgements:

We are very grateful to the following agencies and organisations for finan-cial support: Gobierno de Mendoza, Comision Nacional de Energia Atomicay Municipalidad de Malargue, Argentina; the Australian Research Council;Fundacao de Amparo a Pesquisa do Estado de Sao Paulo, Conselho Na-cional de Desenvolvimento Cientifico e Tecnologico and Fundacao de Amparoa Pesquisa do Estado de Rio de Janeiro, Brasil; National Science Founda-tion of China; Ministry of Education of the Czech Republic (projects LA134and LN00A006); Centre National de la Recherche Scientifique, Institut Na-tional de Physique Nucleaire et Physique des Particules (IN2P3/CNRS), In-stitut National des Sciences de l’Univers (INSU/CNRS) et Conseil RegionalIle de France, France; German Ministry for Education and Research andForschungszentrum Karlsruhe, Germany; Istituto Nazionale di Fisica Nucle-are, Italy; Consejo Nacional de Ciencia y Tecnologia, Mexico; the Polish StateCommittee for Scientific Research (grant numbers 1P03D 01430, 2P03B 11024and 2PO3D 01124), Poland; Slovenian Research Agency; Ministerio de Edu-cacion y Ciencia (FPA2003-08733-C02, 2004-01198), Xunta de Galicia (2003PXIC20612PN, 2005 PXIC20604PN) and Feder Funds, Spain; Particle Physicsand Astronomy Research Council, UK; the US Department of Energy, the USNational Science Foundation, USA, and UNESCO.

AGASA and Yakutsk data [45]; however, the energies reconstructed for the AGASAevents in that work are in conflict with those given by the AGASA group.

26

A Distributions of quality cut variables

In Figure A.1, distributions of cut variables are plotted. For each graph, allquality cuts (see Section 3) except the one for the variable shown were applied.

(core-tank distance [m])10

log1 1.5 2 2.5 3 3.5 4 4.5 5

even

ts

2

4

6

8

10

12

14

data

proton

photon

hybrid tank time residual [ns]0 50 100 150 200 250 300 350 400 450 500

even

ts

-310

-210

-110

1

10

/Ndf2χ0 2 4 6 8 10 12 14

even

ts

-310

-210

-110

1

10

line2χ/

GH2χ

0 0.2 0.4 0.6 0.8 1 1.2

even

ts

2

4

6

8

10

Fig. A.1. Distributions of variables after applying all quality cuts except the one forthe variable shown. The distributions are plotted for data (filled circles), primaryphotons (dashed black histograms), and primary protons (solid blue histograms).The arrow indicates the cut position. Plotted are distributions of distances of thetank with the largest signal to the shower core (upper left panel), of the time residualbetween that tank and the expected arrival time of the shower front (upper rightpanel), of the reduced χ2 from the Gaisser-Hillas profile fit (lower left panel), andof the ratio of this reduced χ2 to that of a straight line fit (lower right panel).

27

B Acceptance correction

The fraction of photons fγ in the cosmic-ray flux integrated above an energythreshold E0 is given by

fγ(E ≥ E0) =

∫

E0

Φγ(E)dE∫

E0Φγ(E)dE +

∑

i

∫

E0Φi(E)dE

(B.1)

where Φγ(E) denotes the differential flux of photons and Φi(E), i = p, He, ...the fluxes of nuclear primaries.

The fraction of photons fdetγ as registered by the detector is given by

fdetγ (E ≥ E0) =

∫

E0Aγ(E)Φγ(E)dE

∫

E0Aγ(E)Φγ(E)dE +

∑

i

∫

EiAi(E)Φi(E)dE

(B.2)

with Aγ(E) and Ai(E) being the detector acceptances to photons and nuclearprimaries, respectively. Ei denotes the effective threshold energy for primarynucleus i.

Thus, the upper limit ful,detγ obtained to the registered data, ful,det

γ > fdetγ ,

needs to be corrected to resemble an upper limit to the fraction of photonsin the cosmic-ray flux. For the present analysis, a conservative and model-independent correction is applied as follows.

E0 corresponds to the analysis threshold energy assuming primary photons.Ei is related to E0 by the ratios of the missing energy corrections mγ (forphotons) and mi (for nuclear primaries),

Ei = E0 ·mi

mγ. (B.3)

Since mγ ≃ 1.01 and mi ≃ 1.07 − 1.14, Ei > E0. Thus, replacing Ei by E0,

fdetγ (E ≥ E0) >

∫

E0Aγ(E)Φγ(E)dE

∫

E0Aγ(E)Φγ(E)dE +

∑

i

∫

E0Ai(E)Φi(E)dE

=

∫

E0Aγ(E)Φγ(E)dE

∫

E0Aγ(E)Φγ(E)dE +

∑

i

∫

E0

Aγ(E)ǫi(E)

Φi(E)dE. (B.4)

In the last step, the acceptance ratio ǫi(E) = Aγ(E)/Ai(E) was introduced.

28

From the fiducial volume cuts shown in Figure 3, it can be seen that Aγ ≃ constin the energy range of interest. Also, from Figure 3 the minimum acceptanceratio ǫmin ≤ ǫi(E) can be extracted (in the current analysis, ǫmin = 0.80).Hence, it follows:

fdetγ (E ≥ E0) >

∫

E0Φγ(E)dE

∫

E0Φγ(E)dE + 1

ǫmin

∑

i

∫

E0Φi(E)dE

> ǫmin ·

∫

E0Φγ(E)dE

∫

E0Φγ(E)dE +

∑

i

∫

E0Φi(E)dE

= ǫmin · fγ(E ≥ E0) , (B.5)

where it was used that 1ǫmin

> 1.

Consequently, an upper limit fulγ to the fraction of photons in the cosmic-ray

flux can conservatively be calculated as

fulγ = ful,det

γ /ǫmin > fdetγ /ǫmin > fγ . (B.6)

The upper limit obtained this way does not depend on assumptions for thedifferential fluxes Φγ(E) and Φi(E).

References

[1] M. Nagano, A.A. Watson, Rev. Mod. Phys. 72, 689 (2000); “Ultimate energyparticles in the Universe”, eds. M. Boratav and G. Sigl, C.R. Physique 5,Elsevier, Paris (2004); J. Cronin, Nucl. Phys. B, Proc. Suppl. 138 (2005), 465.

[2] K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G.T. Zatsepin, V.A. Kuzmin,JETP Lett. 4 78 (1966).

[3] P. Bhattacharjee, G. Sigl, Phys. Rep. 327, 109 (2000).

[4] S. Sarkar, Acta Phys. Polon. B35, 351 (2004).

[5] G. Gelmini, O.E. Kalashev, D.V. Semikoz, [arXiv:astro-ph/0506128].

[6] M. Takeda et al., Astropart. Phys. 19, 447 (2003).

[7] M. Ave et al., Phys. Rev. Lett. 85, 2244 (2000); Phys. Rev. D65, 063007 (2002).

[8] K. Shinozaki et al., Astrophys. J. 571, L117 (2002).

[9] M. Risse et al., Phys. Rev. Lett. 95, 171102 (2005).

[10] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 369(2005).

29

[11] C.T. Hill, Nucl. Phys. B224, 469 (1983); M.B. Hindmarsh, T.W.B. Kibble,Rep. Prog. Phys. 58, 477 (1995).

[12] V. Berezinsky, M. Kachelrieß, A. Vilenkin, Phys. Rev. Lett. 79, 4302 (1997);M. Birkel, S. Sarkar, Astropart. Phys. 9, 297 (1998).

[13] J. Ellis, V. Mayes, D.V. Nanopoulos, [arXiv:astro-ph/0512303].

[14] T.J. Weiler, Phys. Rev. Lett. 49, 234 (1982); T.J. Weiler, Astropart. Phys. 11,303 (1999); D. Fargion, B. Mele, A. Salis, Astrophys. J. 517, 725 (1999).

[15] Z. Fodor, S.D. Katz, Phys. Rev. Lett. 86, 3224 (2001); S. Sarkar, R. Toldra,Nucl. Phys. B621, 495 (2002); C. Barbot, M. Drees, Astropart. Phys. 20,5 (2003); R. Aloisio, V. Berezinsky, M. Kachelrieß, Phys. Rev. D69, 094023(2004).

[16] R.U. Abbasi et al., Phys. Lett. B 619, 271 (2005).

[17] N.N. Kalmykov, S.S. Ostapchenko, A.I. Pavlov, Nucl. Phys. B (Proc. Suppl.)52B, 17 (1997).

[18] S. Ostapchenko, Nucl. Phys. B (Proc. Suppl.) 151, 143 (2006).

[19] R. Engel, T.K. Gaisser, P. Lipari, T. Stanev, Proc. 26th Intern. Cosmic RayConf., Salt Lake City, 415 (1999).

[20] J. Knapp et al., Astropart. Phys. 19, 77 (2003).

[21] L.D. Landau, I.Ya. Pomeranchuk, Dokl. Akad. Nauk SSSR 92, 535 & 735(1953); A.B. Migdal, Phys. Rev. 103, 1811 (1956).

[22] T. Erber, Rev. Mod. Phys. 38, 626 (1966); B. McBreen, C.J. Lambert,Phys. Rev. D 24, 2536 (1981); T. Stanev, H.P. Vankov, Phys. Rev. D 55, 1365(1997).

[23] P. Homola et al., Comp. Phys. Comm. 173, 71 (2005).

[24] D. Heck et al., Reports FZKA 6019 & 6097, Forschungszentrum Karlsruhe(1998).

[25] S. Eidelmann et al., Particle Data Group, Phys. Lett. B592, 1 (2004).

[26] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 13(2005), [arXiv:astro-ph/0508389].

[27] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 1(2005), [arXiv:astro-ph/0508466].

[28] J. Abraham et al., P. Auger Collaboration, Nucl. Instrum. Meth. A 523, 50(2004).

[29] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 17(2005).

30

[30] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 8, 343(2005).

[31] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 8, 5(2005), [arXiv:astro-ph/0507347].

[32] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 123(2005), [arXiv:astro-ph/0507275].

[33] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 8, 347(2005).

[34] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 8, 335(2005).

[35] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 127(2005), [arXiv:astro-ph/0507251]; M. Unger, in preparation (2006).

[36] T.K. Gaisser, A.M. Hillas, Proc. 15th Intern. Cosmic Ray Conf., Plovdiv, 8, 353(1977)

[37] H.M.J. Barbosa et al., Astropart. Phys. 22, 159 (2004).

[38] T. Pierog et al., Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 103 (2005).

[39] T. Bergmann et al., Astropart. Phys., in print (2006), [arXiv:astro-ph/0606564].

[40] L. Prado et al., Nucl. Instr. Meth. A545, 632 (2005).

[41] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Ray Conf., Pune, 7, 283(2005).

[42] T.C. Rogers, M.I. Strikman, [arXiv:hep-ph/0512311].

[43] M. Risse et al., Czech. J. Phys. 56 (2006) A327, [arXiv:astro-ph/0512434].

[44] X. Bertou, P. Billoir, S. Dagoret-Campagne, Astropart. Phys. 14, 121 (2000).

[45] G.I. Rubtsov et al., Phys. Rev. D 73, 063009 (2006).

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